# Optimal packings of bounded degree trees

```@article{Joos2016OptimalPO,
title={Optimal packings of bounded degree trees},
author={Felix Joos and Jaehoon Kim and D. Kuhn and D. Osthus},
journal={arXiv: Combinatorics},
year={2016}
}```
We prove that if \$T_1,\dots, T_n\$ is a sequence of bounded degree trees so that \$T_i\$ has \$i\$ vertices, then \$K_n\$ has a decomposition into \$T_1,\dots, T_n\$. This shows that the tree packing conjecture of Gyarfas and Lehel from 1976 holds for all bounded degree trees (in fact, we can allow the first \$o(n)\$ trees to have arbitrary degrees). Similarly, we show that Ringel's conjecture from 1963 holds for all bounded degree trees. We deduce these results from a more general theorem, which yields… Expand
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